Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#14519827 |
| derived, Sylow | C61 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #6923 |
| commutator, hypocenter | C61 | C4×C32 |
| Frattini | C2×C8 | C2×#6923 |
| Fitting | C4×C8×C61 | C4 |
| socle | C22×C61 | C2×C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C4×C8 | |
72 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14519827, #30594776, #30594778, … |
| maximal normal subgroup of | C8×#14519827, #30594776, #30594778, … |
| maximal quotient of | C8×#14519827, #30594784, #30595080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19614);